HullFund8eCh09ProblemSolutions范本模板.docx
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HullFund8eCh09ProblemSolutions范本模板.docx
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HullFund8eCh09ProblemSolutions范本模板
CHAPTER9
MechanicsofOptionsMarkets
PracticeQuestions
Problem9.8。
Acorporatetreasurerisdesigningahedgingprograminvolvingforeigncurrencyoptions。
Whataretheprosandconsofusing(a)theNASDAQOMXand(b)theover-the—countermarketfortrading?
TheNASDAQOMXoffersoptionswithstandardstrikepricesandtimestomaturity.Optionsintheover—the—countermarkethavetheadvantagethattheycanbetailoredtomeetthepreciseneedsofthetreasurer。
Theirdisadvantageisthattheyexposethetreasurertosomecreditrisk.Exchangesorganizetheirtradingsothatthereisvirtuallynocreditrisk.
Problem9。
9.
SupposethataEuropeancalloptiontobuyasharefor$100。
00costs$5。
00andishelduntilmaturity.Underwhatcircumstanceswilltheholderoftheoptionmakeaprofit?
Underwhatcircumstanceswilltheoptionbeexercised?
Drawadiagramillustratinghowtheprofitfromalongpositionintheoptiondependsonthestockpriceatmaturityoftheoption。
Ignoringthetimevalueofmoney,theholderoftheoptionwillmakeaprofitifthestockpriceatmaturityoftheoptionisgreaterthan$105.Thisisbecausethepayofftotheholderoftheoptionis,inthesecircumstances,greaterthanthe$5paidfortheoption.Theoptionwillbeexercisedifthestockpriceatmaturityisgreaterthan$100.Notethatifthestockpriceisbetween$100and$105theoptionisexercised,buttheholderoftheoptiontakesalossoverall。
TheprofitfromalongpositionisasshowninFigureS9.1.
FigureS9.1ProfitfromlongpositioninProblem9.9
Problem9.10.
SupposethataEuropeanputoptiontosellasharefor$60costs$8andishelduntilmaturity.Underwhatcircumstanceswilltheselleroftheoption(thepartywiththeshortposition)makeaprofit?
Underwhatcircumstanceswilltheoptionbeexercised?
Drawadiagramillustratinghowtheprofitfromashortpositionintheoptiondependsonthestockpriceatmaturityoftheoption。
Ignoringthetimevalueofmoney,theselleroftheoptionwillmakeaprofitifthestockpriceatmaturityisgreaterthan$52.00。
Thisisbecausethecosttotheselleroftheoptionisinthesecircumstanceslessthanthepricereceivedfortheoption.Theoptionwillbeexercisedifthestockpriceatmaturityislessthan$60.00。
Notethatifthestockpriceisbetween$52。
00and$60。
00theselleroftheoptionmakesaprofiteventhoughtheoptionisexercised。
TheprofitfromtheshortpositionisasshowninFigureS9.2.
FigureS9.2ProfitfromshortpositioninProblem9.10
Problem9.11。
Describetheterminalvalueofthefollowingportfolio:
anewlyentered-intolongforwardcontractonanassetandalongpositioninaEuropeanputoptionontheassetwiththesamematurityastheforwardcontractandastrikepricethatisequaltotheforwardpriceoftheassetatthetimetheportfolioissetup.ShowthattheEuropeanputoptionhasthesamevalueasaEuropeancalloptionwiththesamestrikepriceandmaturity。
Theterminalvalueofthelongforwardcontractis:
where
isthepriceoftheassetatmaturityand
istheforwardpriceoftheassetatthetimetheportfolioissetup.(Thedeliverypriceintheforwardcontractisalso
。
)
Theterminalvalueoftheputoptionis:
Theterminalvalueoftheportfolioistherefore
ThisisthesameastheterminalvalueofaEuropeancalloptionwiththesamematurityastheforwardcontractandanexercisepriceequalto
。
ThisresultisillustratedintheFigureS9。
3。
FigureS9.3ProfitfromportfolioinProblem9。
11
Wehaveshownthattheforwardcontractplustheputisworththesameasacallwiththesamestrikepriceandtimetomaturityastheput.Theforwardcontractisworthzeroatthetimetheportfolioissetup.Itfollowsthattheputisworththesameasthecallatthetimetheportfolioissetup。
Problem9。
12。
Atraderbuysacalloptionwithastrikepriceof$45andaputoptionwithastrikepriceof$40。
Bothoptionshavethesamematurity。
Thecallcosts$3andtheputcosts$4。
Drawadiagramshowingthevariationofthetrader’sprofitwiththeassetprice.
FigureS9。
4showsthevariationofthetrader’spositionwiththeassetprice。
Wecandividethealternativeassetpricesintothreeranges:
a)Whentheassetpricelessthan$40,theputoptionprovidesapayoffof
andthecalloptionprovidesnopayoff。
Theoptionscost$7andsothetotalprofitis
。
b)Whentheassetpriceisbetween$40and$45,neitheroptionprovidesapayoff。
Thereisanetlossof$7.
c)Whentheassetpricegreaterthan$45,thecalloptionprovidesapayoffof
andtheputoptionprovidesnopayoff。
Takingintoaccountthe$7costoftheoptions,thetotalprofitis
。
Thetradermakesaprofit(ignoringthetimevalueofmoney)ifthestockpriceislessthan$33orgreaterthan$52.ThistypeoftradingstrategyisknownasastrangleandisdiscussedinChapter11.
FigureS9.4ProfitfromtradingstrategyinProblem9.12
Problem9.13.
ExplainwhyanAmericanoptionisalwaysworthatleastasmuchasaEuropeanoptiononthesameassetwiththesamestrikepriceandexercisedate。
TheholderofanAmericanoptionhasallthesamerightsastheholderofaEuropeanoptionandmore。
Itmustthereforebeworthatleastasmuch。
Ifitwerenot,anarbitrageurcouldshorttheEuropeanoptionandtakealongpositionintheAmericanoption.
Problem9。
14.
ExplainwhyanAmericanoptionisalwaysworthatleastasmuchasitsintrinsicvalue。
TheholderofanAmericanoptionhastherighttoexerciseitimmediately.TheAmericanoptionmustthereforebeworthatleastasmuchasitsintrinsicvalue.Ifitwerenotanarbitrageurcouldlockinasureprofitbybuyingtheoptionandexercisingitimmediately。
Problem9.15。
Explaincarefullythedifferencebetweenwritingaputoptionandbuyingacalloption.
Writingaputgivesapayoffof
。
Buyingacallgivesapayoffof
。
Inbothcasesthepotentialpayoffis
.Thedifferenceisthatforawrittenputthecounterpartychooseswhetheryougetthepayoff(andwillallowyoutogetitonlywhenitisnegativetoyou).Foralongcallyoudecidewhetheryougetthepayoff(andyouchoosetogetitwhenitispositivetoyou.)
Problem9.16.
Thetreasurerofacorporationistryingtochoosebetweenoptionsandforwardcontractstohedgethecorporation’sforeignexchangerisk。
Discusstheadvantagesanddisadvantagesofeach。
Forwardcontractslockintheexchangeratethatwillapplytoaparticulartransactioninthefuture.Optionsprovideinsurancethattheexchangeratewillnotbeworsethansomelevel。
Theadvantageofaforwardcontractisthatuncertaintyiseliminatedasfaraspossible。
Thedisadvantageisthattheoutcomewithhedgingcanbesignificantlyworsethantheoutcomewithnohedging.Thisdisadvantageisnotasmarkedwithoptions.However,unlikeforwardcontracts,optionsinvolveanup—frontcost.
Problem9.17。
Consideranexchange-tradedcalloptioncontracttobuy500shareswithastrikepriceof$40andmaturityinfourmonths.Explainhowthetermsoftheoptioncontractchangewhenthereis
a)A10%stockdividend
b)A10%cashdividend
c)A4—for-1stocksplit
a)Theoptioncontractbecomesonetobuy
shareswithanexerciseprice
。
b)Thereisnoeffect.Thetermsofanoptionscontractarenotnormallyadjustedforcashdividends。
c)Theoptioncontractbecomesonetobuy
shareswithanexercisepriceof40/4=$10.
Problem9。
18.
“Ifmostofthecalloptionsonastockareinthemoney,itislikelythatthestockpricehasrisenrapidlyinthelastfewmonths.”Discussthisstatement.
Theexchangehascertainrulesgoverningwhentradinginanewoptionisinitiated。
Thesemeanthattheoptionisclose-to—the-moneywhenitisfirsttraded.Ifallcalloptionsareinthemoney,itisthereforelikelythatthestockpricehasrisensincetradingintheoptionbegan。
Problem9.19.
Whatistheeffectofanunexpectedcashdividendon(a)acalloptionpriceand(b)aputoptionprice?
Anunexpectedcashdividendwouldreducethestockpriceontheex—dividenddate。
Thisstockpricereductionwouldnotbeanticipatedbyoptionholders.Asaresulttherewouldbeareductioninthevalueofacalloptionandanincreasethevalueofaputoption。
(Notethatthetermsofanoptionareadjustedforcashdividendsonlyinexceptionalcircumstances.)
Problem9.20。
OptionsonGeneralMotorsstockareonaMarch,June,September,andDecembercycle。
Whatoptionstradeon(a)March1,(b)June30,and(c)August5?
a)March,April,JuneandSeptember
b)July,August,September,December
c)August,September,December,March。
Longerdatedoptionsmayalsotrade。
Problem9。
21。
Explainwhythemarketmaker’sbid—offerspreadrepresentsarealcosttooptionsinvestors。
A“fair”pricefortheoptioncanreasonablybeassumedtobehalfwaybetweenthebidandtheofferpricequotedbyamarketmaker。
Aninvestortypicallybuysatthemarketmaker’sofferandsellsatthemarketmaker’sbid.Eachtimeheorshedoesthisthereisahiddencostequaltohalfthebid—offerspread。
Problem9。
22.
AUnitedStatesinvestorwritesfivenakedcalloptioncontracts。
Theoptionpriceis$3.50,thestrikepriceis$60。
00,andthestockpriceis$57.00.Whatistheinitialmarginrequirement?
Thetwocalculationsarenecessarytodeterminetheinitialmargin。
Thefirstgives
Thesecondgives
Theinitialmarginisthegreaterofthese,or$5,950。
Partofthiscanbeprovidedbytheinitialamountof500×3.5=$1,750receivedfortheoptions。
FurtherQuestions
Problem9.23。
Calculatetheintrinsicvalueandtimevaluefromthemid—market(avera
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